What is the integral from-8 to-3 of (-x^2-3x) ?

The integral from-8 to-3 of (-x^2-3x) is -475/6

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integral from-8 to-3 of (-x^2-3x)

\int_{- 8}^{- 3} (- x^{2} - 3 x) d x

- \frac{475}{6}

Decimal

- 79.16666 \dots

Solution steps

\int_{- 8}^{- 3} - x^{2} - 3 x d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= - \int_{- 8}^{- 3} x^{2} d x - \int_{- 8}^{- 3} 3 x d x

\int_{- 8}^{- 3} x^{2} d x = \frac{485}{3}

\int_{- 8}^{- 3} 3 x d x = - \frac{165}{2}

= - \frac{485}{3} - (- \frac{165}{2})

Simplify

- \frac{485}{3} - (- \frac{165}{2}) : - \frac{475}{6}

= - \frac{475}{6}

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What is the integral from-8 to-3 of (-x^2-3x) ?
The integral from-8 to-3 of (-x^2-3x) is -475/6